y^{''}+2y^'=2x+5+e^{-2x}

Lösung

y^{^{''}} + 2 y^{^{'}} = 2 x + 5 + e^{- 2 x}

y = c_{1} + c_{2} e^{- 2 x} + \frac{x ^{2} - e ^{- 2 x} x}{2} + 2 x

Schritte zur Lösung

y^{''} (x) + 2 y^{'} (x) = 2 x + 5 + e^{- 2 x}

Solve linear ODE:

y = c_{1} + c_{2} e^{- 2 x} + \frac{x ^{2} - e ^{- 2 x} x}{2} + 2 x

y = c_{1} + c_{2} e^{- 2 x} + \frac{x ^{2} - e ^{- 2 x} x}{2} + 2 x

y^{^{'''}} - 4 y^{^{'}} = t e^{- 2 t} + 3 cos (2 t)

y^{^{''}} + y^{^{'}} = - 8 e^{- x} - 4

x^{^{''}} + 2 x^{^{'}} + 5 x = 12 cos (2 t) + 3 sin (2 t)

y^{^{''}} + 3 y^{^{'}} - 4 y = 2 cos (x)

y^{^{'''}} - y^{^{''}} - y^{^{'}} + y = 3 e^{- t} + 4